4,232 research outputs found
Interdefinability of defeasible logic and logic programming under the well-founded semantics
We provide a method of translating theories of Nute's defeasible logic into
logic programs, and a corresponding translation in the opposite direction.
Under certain natural restrictions, the conclusions of defeasible theories
under the ambiguity propagating defeasible logic ADL correspond to those of the
well-founded semantics for normal logic programs, and so it turns out that the
two formalisms are closely related. Using the same translation of logic
programs into defeasible theories, the semantics for the ambiguity blocking
defeasible logic NDL can be seen as indirectly providing an ambiguity blocking
semantics for logic programs. We also provide antimonotone operators for both
ADL and NDL, each based on the Gelfond-Lifschitz (GL) operator for logic
programs. For defeasible theories without defeaters or priorities on rules, the
operator for ADL corresponds to the GL operator and so can be seen as partially
capturing the consequences according to ADL. Similarly, the operator for NDL
captures the consequences according to NDL, though in this case no restrictions
on theories apply. Both operators can be used to define stable model semantics
for defeasible theories.Comment: 36 pages; To appear in Theory and Practice of Logic Programming
(TPLP
Aggregated fuzzy answer set programming
Fuzzy Answer Set programming (FASP) is an extension of answer set programming (ASP), based on fuzzy logic. It allows to encode continuous optimization problems in the same concise manner as ASP allows to model combinatorial problems. As a result of its inherent continuity, rules in FASP may be satisfied or violated to certain degrees. Rather than insisting that all rules are fully satisfied, we may only require that they are satisfied partially, to the best extent possible. However, most approaches that feature partial rule satisfaction limit themselves to attaching predefined weights to rules, which is not sufficiently flexible for most real-life applications. In this paper, we develop an alternative, based on aggregator functions that specify which (combination of) rules are most important to satisfy. We extend upon previous work by allowing aggregator expressions to define partially ordered preferences, and by the use of a fixpoint semantics
Towards Closed World Reasoning in Dynamic Open Worlds (Extended Version)
The need for integration of ontologies with nonmonotonic rules has been
gaining importance in a number of areas, such as the Semantic Web. A number of
researchers addressed this problem by proposing a unified semantics for hybrid
knowledge bases composed of both an ontology (expressed in a fragment of
first-order logic) and nonmonotonic rules. These semantics have matured over
the years, but only provide solutions for the static case when knowledge does
not need to evolve. In this paper we take a first step towards addressing the
dynamics of hybrid knowledge bases. We focus on knowledge updates and,
considering the state of the art of belief update, ontology update and rule
update, we show that current solutions are only partial and difficult to
combine. Then we extend the existing work on ABox updates with rules, provide a
semantics for such evolving hybrid knowledge bases and study its basic
properties. To the best of our knowledge, this is the first time that an update
operator is proposed for hybrid knowledge bases.Comment: 40 pages; an extended version of the article published in Theory and
Practice of Logic Programming, 10 (4-6): 547 - 564, July. Copyright 2010
Cambridge University Pres
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